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Journal ArticleDOI

Vibration analysis of laminated conical shells with variable thickness

08 Aug 1991-Journal of Sound and Vibration (JOURNAL OF SOUND AND VIBRATION)-Vol. 148, Iss: 3, pp 477-491
TL;DR: In this article, the effects of thickness variation on natural frequencies of laminated conical shells have been studied by using a semi-analytical finite element method, where Love's first approximation thin shell theory is used to solve the problem.
About: This article is published in Journal of Sound and Vibration.The article was published on 1991-08-08. It has received 52 citations till now. The article focuses on the topics: Shell (structure) & Radius.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the nonaxisymmetric vibrations of an inhomogeneous conical shell of variable thickness under a nonstationary load is formulated and solved using Timoshenko-type shell theory.
Abstract: The problem of the nonaxisymmetric vibrations of an inhomogeneous conical shell of variable thickness under a nonstationary load is formulated and solved An algorithm for solving this problem is presented The system of differential equations is solved using Timoshenko-type shell theory The dynamic behavior of a conical panel of variable thickness under a nonstationary load is analyzed as an example

Cites background from "Vibration analysis of laminated con..."

  • ...The free vibrations of shells (mainly cylindrical, conical, and spherical) of variable thickness were classically studied in [7–10, 14–17]....

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Journal ArticleDOI
30 Dec 2020
TL;DR: In this article, the authors studied the natural frequencies of circular truncated conical shells, the thickness of which varies along the length according to different laws, and the behavior of elastic structure is described in the framework of the classical theory of shells based on the Kirchhoff-love hypotheses.
Abstract: The paper presents the results of studying the natural frequencies of circular truncated conical shells, the thickness of which varies along the length according to different laws. The behavior of elastic structure is described in the framework of the classical theory of shells based on the Kirchhoff-Love hypotheses. The corresponding geometric and physical relations together with the equations of motion are reduced to a system of ordinary differential equations for new unknowns. The solution to the formulated boundary value problem is found using Godunov's orthogonal sweep method involving the numerical integration of differential equations by the fourth order Runge-Kutta method. The natural frequencies of vibrations are evaluated using a combination of a step-wise procedure and subsequent refinement by the interval bisection method. The reliability of the obtained results is verified by making a comparison with the known numerical-analytical solutions. The dependences of the minimum vibration frequencies obtained at shell thicknesses subject to a power-law variation (linear and quadratic, having symmetric and asymmetric shapes) and harmonic variation (with positive and negative curvature) are investigated for shells with different combinations of boundary conditions (free support, rigid and cantilever fastening), cone angles and linear dimensions. The results of the study confirm the existence of configurations, which provide a significant increase in the frequency spectrum in comparison with shells of constant thickness under the same limitations on the weight of the structure.
Journal ArticleDOI
20 Jul 2022
TL;DR: In this paper , an analytical model is developed to investigate the buckling analysis of the composite sandwich conical shell with variable skin thickness under lateral pressure loading, where an effective smeared method is employed to reduce the reinforced lattice core into a layer.
Abstract: In this paper, an analytical model is developed to investigate the buckling analysis of the composite sandwich conical shell with variable skin thickness under lateral pressure loading. This problem involves composite shells, which are produced during the filament-winding process, where the skin thickness varies through the length of the shell. An effective smeared method is employed to reduce the reinforced lattice core into a layer. This is done by analyzing forces and moments on a unit cell. Therefore, equivalent stiffness parameters of reinforced lattice core are determined. By superimposing stiffness parameters due to the lattice core with those of the inner and outer skins, the equivalent stiffness of the sandwich panel will be obtained. Governing equations are established based on the first shear deformation theory. The power series method is used to extract the buckling load of the stiffened shell. To verify achieved results, a 3D finite element model is provided. Comparisons showed that the analytical solution is qualified enough to study the buckling behavior of the composite sandwich conical shell. Through this study, the effects of a set of important parameters like stiffener orientation angle, number of stiffeners, semi-vertex angle, and skin lamination are investigated.
Journal ArticleDOI
01 Jun 2019
TL;DR: In this paper, a layerwise-differential quadrature method (LW-DQM) is developed for the vibration analysis of a stiffened laminated conical shell.
Abstract: A layerwise-differential quadrature method (LW-DQM) is developed for the vibration analysis of a stiffened laminated conical shell. The circumferential stiffeners (rings) and meridional stiffeners (stringers) are treated as discrete elements. The motion equations are derived by applying the Hamilton’s principle. In order to accurately account for the thickness effects and the displacement field of stiffeners, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations applying the DQM in the meridional direction. The advantage of the proposed model is its applicability to thin and thick unstiffened and stiffened shells with arbitrary boundary conditions. In addition, the axial load and external pressure is applied to the shell as a ratio of the global buckling load and pressure. This study demonstrates the accuracy, stability, and the fast rate of convergence of the present method, for the buckling and vibration analyses of stiffened conical shells. The presented results are compared with those of other shell theories and a special case where the angle of conical shell approaches zero, i.e. a cylindrical shell, and excellent agreements are achieved.
References
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Journal ArticleDOI
TL;DR: In this paper, the free vibration analysis of joined conical-cylindrical shells is presented, where the governing equations of vibration of a conical shell, including a cylindrical shell as a special case, are written as a coupled set of first order differential equations by using the transfer matrix of the shell.

129 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a survey of the structural mechanics of composite materials, focusing on the macromechanical structural analysis of various structural elements, including response under conditions of stable static loading, buckling, and dynamics.
Abstract: Introduction T purpose of this Survey is to review and bring together in an orderly fashion some of the principal contributions to the field of structural mechanics of structures containing composite materials. The topics of micromechanics and fracture, while quite important, are not considered in this Survey. Emphasis is given to the macromechanical structural analysis of various structural elements, including response under conditions of stable static loading, buckling, and dynamics. The Survey unfolds in the following sequence: Straight and Curved Laminated Bars, Laminated Plates, Laminated Shells, Sandwich Structures, Applications to Practical Structural Systems, and Future Trends. The authors hope that this contribution will be a useful reference tool for researchers and engineers already involved in structural aspects of advanced composites, as well as for those who are just entering the field. No Survey can do full justice to such a wide field as compositematerial structural mechanics. The references cited give only a glimpse of the extensive literature in this field. The authors apologize for not citing a number of important contributions in the field.

115 citations

Journal ArticleDOI
TL;DR: In this paper, the free vibration of a truncated conical shell with variable thickness was analyzed by using the transfer matrix approach, and the effects of the semi-vertex angle, truncated length and varying thickness on the vibration were studied.

105 citations

Journal ArticleDOI
TL;DR: In this article, an analysis of axisymmetric and unsymmetric free vibrations of conical or cylindrical shells with various boundary conditions is presented, where Love's first-approximation shell theory, with transverse shear strain added, was used and solutions were obtained by Galerkin's method.

78 citations